Question 1

Use the Factor Theorem to show that $( x - 4 )$ 
is a factor of the polynomial. $P ( x ) = x ^ { 5 } + x ^ { 4 } - 36 x ^ { 3 } - 16 x ^ { 2 } + 320 x$

Accepted Answer

@#LAT-DLM& 
is a fac

Question 2

Find a polynomial of degree 3 with constant coefficient $- 18$ 
and zeros $- 1$ , $- 2$ , and $3$ 
.

Accepted Answer

The answer of Find a polynomial of degree 3 with...

Question 3

Find all rational, irrational, and complex zeros (and state their multiplicities). $p ( x ) = x ^ { 3 } - x ^ { 2 } - 2 x + 2$

Accepted Answer

A)  $\{ - \sqrt { 2 } i , \sqrt { 2 } i , 2 \}$ 
B)  $\{ - \sqrt { 2 } i , \sqrt { 2 } i , 1 \}$ 
C)  $\{ - 2,2,1 \}$ 
D)  $\{ - \sqrt { 2 } , \sqrt { 2 } , 1 \}$ 
E)  $( - 1 , - 2 \}$ 
A)  $\{ - \sqrt { 2 } i , \sqrt { 2 } i , 2 \}$ 
B)  $\{ - \sqrt { 2 } i , \sqrt { 2 } i , 1 \}$ 
C)  $\{ - 2,2,1 \}$ 
D)  $\{ - \sqrt { 2 } , \sqrt { 2 } , 1 \}$ 
E)  $( - 1 , - 2 \}$

Question 4

Find the indicated value of the polynomial using the Remainder Theorem. $p ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 11 x - 100$ 
; find $p ( 3 )$

Accepted Answer

None

Question 5

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 9 x ^ { 4 } + 9 } { x ^ { 2 } + 9 }$

Accepted Answer

quotient:

Question 6

Find the quotient and remainder. $\frac { x ^ { 2 } + x - 5 } { x + 6 }$

Accepted Answer

@#LAT-DLM& 
; Quotie

Question 7

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 4 x ^ { 4 } + 4 } { x ^ { 2 } + 4 }$

Accepted Answer

quotient:

Question 8

Use a graphing device to graph the polynomial $y = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1$ 
and describe its end behavior.

Accepted Answer

The answer of Use a graphing device to graph the...

Question 9

Evaluate the expression $( 4 - i ) ( 4 + i )$ and write in the form $a + b i$

Accepted Answer

A)  $16 i$ 
B)  $17 - 0 i$ 
C)  $8 + i$ 
D)  $8 - i$ 
A)  $16 i$ 
B)  $17 - 0 i$ 
C)  $8 + i$ 
D)  $8 - i$

Question 10

Evaluate the expression and write the result in the form a + bi. $\left( 7 - \frac { 5 } { 2 } i \right) - \left( 5 + \frac { 7 } { 2 } i \right)$

Accepted Answer

The answer of Evaluate the expression and write the result...

Question 11

Find all real and complex zeros of $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 8$

Accepted Answer

The answer of Find all real and complex zeros of...

Question 12

Use a graphing device to graph the polynomial $p ( x ) = 3 x ^ { 4 } - 4 x ^ { 3 } - 10 x$ to describe its end behavior

Accepted Answer

A)  $p ( x ) \rightarrow 0$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty $ 
B)  $p ( x ) \rightarrow \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow 0$As $x \rightarrow - \infty$ 
C)  $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow - \infty$As $x \rightarrow - \infty 3$ 
D)  $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$ 
E)  $p ( x ) \rightarrow \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty $ 
A)  $p ( x ) \rightarrow 0$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty $ 
B)  $p ( x ) \rightarrow \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow 0$As $x \rightarrow - \infty$ 
C)  $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow - \infty$As $x \rightarrow - \infty 3$ 
D)  $p ( x ) \rightarrow - \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty$ 
E)  $p ( x ) \rightarrow \infty$As $x \rightarrow \infty$
; $p ( x ) \rightarrow \infty$As $x \rightarrow - \infty $

Question 13

If a ball is thrown directly upward with a velocity of 64 ft/s, its height (in feet) after t seconds is givenby $y = 64 t - 16 t ^ { 2 }$  . What is the maximum height attained by the ball?

Accepted Answer

The answer of If a ball is thrown directly upward...

Question 14

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. $y ( x ) = \frac { 2 x ^ { 2 } + 3 x } { x ^ { 2 } + x - 2 }$

Accepted Answer

The answer of Graph the rational function. Show clearly all...

Question 15

Find the indicated value of the polynomial using the Remainder Theorem. $P ( x ) = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1$ ; find $p ( - 2 )$

Accepted Answer

A)  $- 2$ 
B)  $- 47$ 
C)  $73$ 
D)  $- 73$ 
E)  $2$ 
A)  $- 2$ 
B)  $- 47$ 
C)  $73$ 
D)  $- 73$ 
E)  $2$

Question 16

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 11 x + 30 }$

Accepted Answer

@#LAT-DLM&  as @#LAT-DLM&  , so @#LAT-DLM& 
is the

Question 17

Find the quotient and remainder. $\frac { x ^ { 3 } - 2 x ^ { 2 } + x - 3 } { x - 3 }$

Accepted Answer

A)  Quotient: $x ^ { 2 } - x + 3$
; Remainder: $- 6$ 
B)  Quotient: $x ^ { 2 } + x + 4$
; Remainder: $9$ 
C)  Quotient: $9$
; Remainder: $x ^ { 2 } - x - 4$ 
D)  Quotient: $x ^ { 2 } + x - 4$
; Remainder: $- 3$ 
E)  Quotient: $x - 3$
; Remainder: $12$ 
A)  Quotient: $x ^ { 2 } - x + 3$
; Remainder: $- 6$ 
B)  Quotient: $x ^ { 2 } + x + 4$
; Remainder: $9$ 
C)  Quotient: $9$
; Remainder: $x ^ { 2 } - x - 4$ 
D)  Quotient: $x ^ { 2 } + x - 4$
; Remainder: $- 3$ 
E)  Quotient: $x - 3$
; Remainder: $12$

Question 18

Evaluate the expression and write in the form $a + b i$ 
. $i ^ { 37 }$

Accepted Answer

The answer of Evaluate the expression and write in the...

Question 19

A quadratic function is given. (a) Express the quadratic function in standard form
b) Find its vertex and its x- and y-intercept(s). $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

Accepted Answer

(a) @#LAT-DLM& 
b) vertex: @#LAT-DLM& 
,

Question 20

Find the remainder if $p ( x ) = 6 x ^ { 342 } + 18 x ^ { 63 } - 5 x ^ { 2 } - 20$  is divided by $( x - 1 )$

Accepted Answer

If @#LAT-DLM&  is di

Use the Factor Theorem to show that $( x - 4 )$ is a factor of the polynomial. $P ( x ) = x ^ { 5 } + x ^ { 4 } - 36 x ^ { 3 } - 16 x ^ { 2 } + 320 x$

Find a polynomial of degree 3 with constant coefficient $- 18$ and zeros $- 1$ , $- 2$ , and $3$ .

Find all rational, irrational, and complex zeros (and state their multiplicities). $p ( x ) = x ^ { 3 } - x ^ { 2 } - 2 x + 2$

Find the indicated value of the polynomial using the Remainder Theorem. $p ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 11 x - 100$ ; find $p ( 3 )$

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 9 x ^ { 4 } + 9 } { x ^ { 2 } + 9 }$

Find the quotient and remainder. $\frac { x ^ { 2 } + x - 5 } { x + 6 }$

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 4 x ^ { 4 } + 4 } { x ^ { 2 } + 4 }$

Use a graphing device to graph the polynomial $y = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1$ and describe its end behavior.

Evaluate the expression $( 4 - i ) ( 4 + i )$ and write in the form $a + b i$

Evaluate the expression and write the result in the form a + bi. $\left( 7 - \frac { 5 } { 2 } i \right) - \left( 5 + \frac { 7 } { 2 } i \right)$

Find all real and complex zeros of $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 8$

Use a graphing device to graph the polynomial $p ( x ) = 3 x ^ { 4 } - 4 x ^ { 3 } - 10 x$ to describe its end behavior

If a ball is thrown directly upward with a velocity of 64 ft/s, its height (in feet) after t seconds is givenby $y = 64 t - 16 t ^ { 2 }$ . What is the maximum height attained by the ball?

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. $y ( x ) = \frac { 2 x ^ { 2 } + 3 x } { x ^ { 2 } + x - 2 }$

Find the indicated value of the polynomial using the Remainder Theorem. $P ( x ) = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1$ ; find $p ( - 2 )$

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 11 x + 30 }$

Find the quotient and remainder. $\frac { x ^ { 3 } - 2 x ^ { 2 } + x - 3 } { x - 3 }$

Evaluate the expression and write in the form $a + b i$ . $i ^ { 37 }$

A quadratic function is given. (a) Express the quadratic function in standard form b) Find its vertex and its x- and y-intercept(s). $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

Find the remainder if $p ( x ) = 6 x ^ { 342 } + 18 x ^ { 63 } - 5 x ^ { 2 } - 20$ is divided by $( x - 1 )$

Equations and Graphs

Functions

Polynomial and Rational Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 4: Exponential and Logarithmic Functions

Use the Factor Theorem to show that (x−4)( x - 4 )(x−4) is a factor of the polynomial. P(x)=x5+x4−36x3−16x2+320xP ( x ) = x ^ { 5 } + x ^ { 4 } - 36 x ^ { 3 } - 16 x ^ { 2 } + 320 xP(x)=x5+x4−36x3−16x2+320x

Find a polynomial of degree 3 with constant coefficient −18- 18−18 and zeros −1- 1−1 , −2- 2−2 , and 333 .

Find all rational, irrational, and complex zeros (and state their multiplicities). p(x)=x3−x2−2x+2p ( x ) = x ^ { 3 } - x ^ { 2 } - 2 x + 2p(x)=x3−x2−2x+2

Find the indicated value of the polynomial using the Remainder Theorem. p(x)=2x3−2x2+11x−100p ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 11 x - 100p(x)=2x3−2x2+11x−100 ; find p(3)p ( 3 )p(3)

Find the quotient and remainder using long division. x6+x2+9x4+9x2+9\frac { x ^ { 6 } + x ^ { 2 } + 9 x ^ { 4 } + 9 } { x ^ { 2 } + 9 }x2+9x6+x2+9x4+9​

Find the quotient and remainder. x2+x−5x+6\frac { x ^ { 2 } + x - 5 } { x + 6 }x+6x2+x−5​

Find the quotient and remainder using long division. x6+x2+4x4+4x2+4\frac { x ^ { 6 } + x ^ { 2 } + 4 x ^ { 4 } + 4 } { x ^ { 2 } + 4 }x2+4x6+x2+4x4+4​

Use a graphing device to graph the polynomial y=2x5+3x2−2x+1y = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1y=2x5+3x2−2x+1 and describe its end behavior.

Evaluate the expression (4−i)(4+i)( 4 - i ) ( 4 + i )(4−i)(4+i) and write in the form a+bia + b ia+bi

Evaluate the expression and write the result in the form a + bi. (7−52i)−(5+72i)\left( 7 - \frac { 5 } { 2 } i \right) - \left( 5 + \frac { 7 } { 2 } i \right)(7−25​i)−(5+27​i)

Find all real and complex zeros of P(x)=x3−2x2−6x−8P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 8P(x)=x3−2x2−6x−8

Use a graphing device to graph the polynomial p(x)=3x4−4x3−10xp ( x ) = 3 x ^ { 4 } - 4 x ^ { 3 } - 10 xp(x)=3x4−4x3−10x to describe its end behavior

If a ball is thrown directly upward with a velocity of 64 ft/s, its height (in feet) after t seconds is givenby y=64t−16t2y = 64 t - 16 t ^ { 2 }y=64t−16t2 . What is the maximum height attained by the ball?

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. y(x)=2x2+3xx2+x−2y ( x ) = \frac { 2 x ^ { 2 } + 3 x } { x ^ { 2 } + x - 2 }y(x)=x2+x−22x2+3x​

Find the indicated value of the polynomial using the Remainder Theorem. P(x)=2x5+3x2−2x+1P ( x ) = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1P(x)=2x5+3x2−2x+1 ; find p(−2)p ( - 2 )p(−2)

Find all horizontal and vertical asymptotes of the function y(x)=x2x2−11x+30y ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 11 x + 30 }y(x)=x2−11x+30x2​

Find the quotient and remainder. x3−2x2+x−3x−3\frac { x ^ { 3 } - 2 x ^ { 2 } + x - 3 } { x - 3 }x−3x3−2x2+x−3​

Evaluate the expression and write in the form a+bia + b ia+bi . i37i ^ { 37 }i37

A quadratic function is given. (a) Express the quadratic function in standard form b) Find its vertex and its x- and y-intercept(s). f(x)=2x2+8x+9f ( x ) = 2 x ^ { 2 } + 8 x + 9f(x)=2x2+8x+9

Find the remainder if p(x)=6x342+18x63−5x2−20p ( x ) = 6 x ^ { 342 } + 18 x ^ { 63 } - 5 x ^ { 2 } - 20p(x)=6x342+18x63−5x2−20 is divided by (x−1)( x - 1 )(x−1)

Equations and Graphs

Functions

Polynomial and Rational Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Use the Factor Theorem to show that $( x - 4 )$ is a factor of the polynomial. $P ( x ) = x ^ { 5 } + x ^ { 4 } - 36 x ^ { 3 } - 16 x ^ { 2 } + 320 x$

Find a polynomial of degree 3 with constant coefficient $- 18$ and zeros $- 1$ , $- 2$ , and $3$ .

Find all rational, irrational, and complex zeros (and state their multiplicities). $p ( x ) = x ^ { 3 } - x ^ { 2 } - 2 x + 2$

Find the indicated value of the polynomial using the Remainder Theorem. $p ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 11 x - 100$ ; find $p ( 3 )$

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 9 x ^ { 4 } + 9 } { x ^ { 2 } + 9 }$

Find the quotient and remainder. $\frac { x ^ { 2 } + x - 5 } { x + 6 }$

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 4 x ^ { 4 } + 4 } { x ^ { 2 } + 4 }$

Use a graphing device to graph the polynomial $y = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1$ and describe its end behavior.

Evaluate the expression $( 4 - i ) ( 4 + i )$ and write in the form $a + b i$

Evaluate the expression and write the result in the form a + bi. $\left( 7 - \frac { 5 } { 2 } i \right) - \left( 5 + \frac { 7 } { 2 } i \right)$

Find all real and complex zeros of $P ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 8$

Use a graphing device to graph the polynomial $p ( x ) = 3 x ^ { 4 } - 4 x ^ { 3 } - 10 x$ to describe its end behavior

If a ball is thrown directly upward with a velocity of 64 ft/s, its height (in feet) after t seconds is givenby $y = 64 t - 16 t ^ { 2 }$ . What is the maximum height attained by the ball?

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. $y ( x ) = \frac { 2 x ^ { 2 } + 3 x } { x ^ { 2 } + x - 2 }$

Find the indicated value of the polynomial using the Remainder Theorem. $P ( x ) = 2 x ^ { 5 } + 3 x ^ { 2 } - 2 x + 1$ ; find $p ( - 2 )$

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 11 x + 30 }$

Find the quotient and remainder. $\frac { x ^ { 3 } - 2 x ^ { 2 } + x - 3 } { x - 3 }$

Evaluate the expression and write in the form $a + b i$ . $i ^ { 37 }$

A quadratic function is given. (a) Express the quadratic function in standard form b) Find its vertex and its x- and y-intercept(s). $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

Find the remainder if $p ( x ) = 6 x ^ { 342 } + 18 x ^ { 63 } - 5 x ^ { 2 } - 20$ is divided by $( x - 1 )$